Given: the distance between the foci = 13 and conjugate axis is 5

To find: the equation of the hyperbola

Formula used:

For hyperbola:

Distance between the foci is 2ae and b² = a²(e² – 1)

Length of conjugate axis is 2b

Therefore

2ae = 13

b² = a²(e² – 1)

⇒ b² = a²e² – a²

Equation of hyperbola is:

Hence, required equation of hyperbola is 25x² – 144y² = 900